Geodesic
Strong limit theorems for increments of sums of independent random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 7, Tome 311 (2004), pp. 260-285 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We derive universal strong laws for increments of sums of independent nonidentically distributed random variables. These results generalize universal results of the author for i.i.d. case which include the strong law of large numbers, the law of the iterated logarithm, the Erdős–Rényi law and the Csörgő–Révész laws. 
@article{ZNSL_2004_311_a15,
     author = {A. N. Frolov},
     title = {Strong limit theorems for increments of sums of independent random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {260--285},
     year = {2004},
     volume = {311},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_311_a15/}
}
TY  - JOUR
AU  - A. N. Frolov
TI  - Strong limit theorems for increments of sums of independent random variables
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2004
SP  - 260
EP  - 285
VL  - 311
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2004_311_a15/
LA  - ru
ID  - ZNSL_2004_311_a15
ER  - 
%0 Journal Article
%A A. N. Frolov
%T Strong limit theorems for increments of sums of independent random variables
%J Zapiski Nauchnykh Seminarov POMI
%D 2004
%P 260-285
%V 311
%U http://geodesic.mathdoc.fr/item/ZNSL_2004_311_a15/
%G ru
%F ZNSL_2004_311_a15
A. N. Frolov. Strong limit theorems for increments of sums of independent random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 7, Tome 311 (2004), pp. 260-285. http://geodesic.mathdoc.fr/item/ZNSL_2004_311_a15/

[1] P. Erdős, A. Rényi, “On a new law of large numbers”, J. Anal. Math., 23 (1970), 103–111 | DOI | MR | Zbl

[2] L. A. Shepp, “A limit law concerning moving averages”, Ann. Math. Statist., 35 (1964), 424–428 | DOI | MR | Zbl

[3] S. Csörgő, “Erdős–Rényi laws”, Ann. Statist., 7 (1979), 772–787 | DOI | MR

[4] D. M. Mason, “An extended version of the Erdős–Rényi strong law of large numbers”, Ann. Probab., 17 (1989), 257–265 | DOI | MR | Zbl

[5] M. Csörgő, P. Révész, Strong approximations in probability and statistics, Budapest, 1981 | MR | Zbl

[6] N. M. Zinchenko, “Asimptotika priraschenii ustoichivykh sluchainykh protsessov so skachkami odnogo znaka”, Teoriya veroyatn. i ee primen., 32:4 (1987), 793–796 | MR

[7] A. N. Frolov, “On one-sided strong laws for large increments of sums”, Statist. Probab. Lett., 37 (1998), 155–165 | DOI | MR | Zbl

[8] A. N. Frolov, “Ob asimptoticheskom povedenii priraschenii summ nezavisimykh sluchainykh velichin”, DAN, 372:5 (2000), 596–599 | MR | Zbl

[9] A. N. Frolov, “On one-sided strong laws for increments of sums of i.i.d. random variables”, Studia Sci. Math. Hungar., 39 (2002), 333–359 | MR | Zbl

[10] A. N. Frolov, “Predelnye teoremy dlya priraschenii summ nezavisimykh sluchainykh velichin”, Teor. veroyatn. i ee primen., 48:1 (2003), 104–121 | MR | Zbl

[11] S. A. Book, “A version of the Erdős–Rényi law of large numbers for independent random variables”, Bull. Inst. Math. Acad. Sinica, 3:2 (1975), 199–211 | MR | Zbl

[12] S. A. Book, “Large deviation probabilities and the Erdös–Rényi law of large numbers”, Canad. J. Statist., 4 (1976), 185–210 | DOI | MR | Zbl

[13] Z. Y. Lin, “The Erdős–Rényi laws of large numbers for nonidentically distributed random variables”, Chin. Ann. Math., 11 (1990), 376–383 | MR | Zbl

[14] Z. Y. Lin, C. R. Lu, Q. M. Shao, “Contribution to the limit theorems”, Contemporary Math., 118 (1991), 221–237 | MR | Zbl

[15] D. L. Hanson, R. P. Russo, “Some limit results for lag sums of independent, non-i.i.d. random variables”, Z. Wahrsch. Verw. Geb., 68 (1985), 425–445 | DOI | MR | Zbl

[16] A. N. Frolov, “O zakone bolshikh chisel Erdesha–Reni pri narushenii usloviya Kramera dlya nezavisimykh neodinakovo raspredelennykh sluchainykh velichin”, Vestn. LGU, 8 (1991), 57–61

[17] A. N. Frolov, “Ob asimptoticheskom povedenii priraschenii summ nezavisimykh sluchainykh velichin”, Vestn. SPbGU, 22 (1993), 45–48

[18] A. N. Frolov, A. I. Martikainen, J. Steinebach, “Erdős–Rényi–Shepp type laws in noni.i.d. case”, Studia Sci. Math. Hungar., 33 (1997), 127–151 | MR | Zbl

[19] Z. Cai, “Strong approximation and improved Erdős–Rényi laws for sums of independent nonidentically distributed random variables”, J. Hangzhou Univ., 19:3 (1992), 240–246 | MR | Zbl

[20] A. N. Frolov, “Ob asimptoticheskom povedenii bolshikh priraschenii summ nezavisimykh sluchainykh velichin”, Teor. veroyatn. i ee primenen., 47:2 (2002), 366–374 | MR | Zbl

[21] A. N. Frolov, “On asymptotics of large increments of sums in non-i.i.d. case”, Acta Applicandae Mathematicae, 78 (2003), 129–136 | DOI | MR | Zbl

[22] V. V. Petrov, Predelnye teoremy dlya summ nezavisimykh sluchainykh velichin, Nauka, M., 1987 | MR

[23] V. M. Zolotarev, Odnomernye ustoichivye raspredeleniya, Nauka, M., 1983 | MR

[24] A. N. Frolov, “O zakone bolshikh chisel Erdesha–Reni dlya protsessov vosstanovleniya”, Teor. veroyatn. i matem. stat., 68 (2003), 142–151 | MR | Zbl

[25] A. I. Sakhanenko, “Skorost skhodimosti v printsipe invariantnosti dlya raznoraspredelennykh velichin s eksponentsialnymi momentami”, Predelnye teoremy dlya summ sluchainykh velichin, Tr. in–ta matematiki Sib. otd. AN SSSR, 3, 1984, 4–49 | MR | Zbl

[26] W. Feller, “Limit theorems for probabilities of large deviations”, Z. Wahrsch. Verw. Geb., 14 (1969), 1–20 | DOI | MR | Zbl